The present invention relates to optical measurement devices, and more particularly to a method of high accuracy calibration of complete polarimeters.
Commercially available polarimeters work either with only a detector and a rotatable wave plate or they are based on a multi-detector arrangement with four (or more) detectors. Complete polarimeters are polarimeters that measure all four Stokes parameters. On multi-detector polarimeters, the incident light power is broken down into at least four separate power components. At least three of the four power components pass polarising elements and thus become polarisation-dependent. One or several birefringent elements, which are arranged in front of the polarising elements, ensure that the maxima of the four detector currents occur at different input polarisations.
A 4×4 calibration matrix B for the polarimeter gives a clear connection between the four detector currents I0 . . . I3 and the four Stokes parameters S0 . . . S3.S=B*I
A four-detector polarimeter allows the parameters—(1) state of polarisation (SOP), (2) degree of polarisation (DOP) and (3) power of the light—to be measured from four measured detector currents. The parameters are derivable from the four Stokes parameters S0 S1, S2 and S3. S0is the total power, S1, S2 and S3 are usually normalised to the total power, so that the normalised Stokes parameters s1,s2 and s3 indicate the state of polarisation.
The degree of polarisation marks the ratio of the polarised power to the total power and is described by the formula   DOP  =            SQRT      ⁡              (                              S            1            2                    +                      S            2            2                    +                      S            3            2                          )              /          S      0      A complete description of the polarisation characteristics of the light is provided mathematically with the help of the Stokes vector.
The Stokes vector is fully determined by the four Stokes parameters S0 . . . S3, which are defined as follows: S0 is the total power, S1 is the component linearly polarised horizontally minus the component linearly polarised vertically, S2 is the component polarised linearly at 45° minus the component polarised linearly at −45°, S3 is the right circularly polarised component minus the left circularly polarised component.
A wave plate has a direction-dependent refractive index. Thus the generally linear partial waves experience different phase velocities and attain a phase difference, which changes their state of polarisation. A polariser dampens the partial wave in its reverse direction more strongly than the orthogonal component in the forward direction. Thus the transmitted light power becomes polarisation-dependent and a simple detection of the polarisation is made possible.
Polarimeters are employed e.g. for the following applications:                Determination of the polarisation, the power and the degree of polarisation (DOP)        Determination of the degree of polarisation (DOP) as a control signal for a PMD compensation        Determination of the polarisation-dependent loss (PDL) of optical fibres and optical components        Determination of the polarisation mode dispersion (PMD) of optical fibres and optical components        Analysis of birefringent and polarising materials        Determination of the extinction ratio (ER) for polarisation-maintaining fibres (PMF)        Evaluation of sensors on a polarimetric basis (e.g. Faraday current sensor)        Generation of control signals in automatic polarisation controllers        and much more        
Apart from complete polarimeters, which measure all four Stokes parameters, there are devices which only determine the deviation of the polarisation from a specified condition. This task is performed already by simple polarisers, polarisation beam splitters etc.
For the calibration of a polarimeter, known states of polarisation and optical powers are usually fed into the polarimeter, and the associated detector signals are measured. From the known states of polarisation and the associated detector signals, a transmission function (calibration matrix) is calculated. The optical input signals must usually be known with a high precision.
In R. M. A. Azzam et al: “Construction, calibration and testing of a four-detector photopolarimeter”, Review of Scientific Instruments, Vol. 59, No. 1, January, 1988, New York, U.S. pp. 84-88, the procedure for a usual “Four Point Calibration” is described. For the calibration of the polarimeters, four polarisations with known Stokes parameters Si,j are employed. The control variable i describes the corresponding Stokes parameter of the state of polarisation j. The four Stokes vectors are placed into the columns of matrix S. For each of the four known input polarisations, the four detector currents are measured and entered into the columns of matrix I.
The instrument matrix A is given by:A=I*S−1Generally, the linear-horizontal (H), linear−45°(45°), circular-right (R) and linear-vertical (V) states of polarisation are employed. For the matrix S, it thus follows:   S  =      [                            1                          1                          1                          1                                      1                          0                          0                                      -            1                                                0                          1                          0                          0                                      0                          0                          1                          0                      ]  
Generally, however, the calibration can be performed at any four polarisations which are not on the same plane. In addition there is the demand that the power be constant and the DOP be equal to 1 (DOP=100%). Following normalisation to the constant power, the following then applies to the four Stokes vectors:                                                                         S                0                2                            =                                                S                  1                  2                                +                                  S                  2                  2                                +                                  S                  3                  2                                                                                                        S              =                              [                                                                            1                                                              1                                                              1                                                              1                                                                                                                          S                                                  1                          ,                          0                                                                                                                                    S                                                  1                          ,                          1                                                                                                                                    S                                                  1                          ,                          2                                                                                                                                    S                                                  1                          ,                          3                                                                                                                                                                        S                                                  2                          ,                          0                                                                                                                                    S                                                  2                          ,                          1                                                                                                                                    S                                                  2                          ,                          2                                                                                                                                    S                                                  2                          ,                          3                                                                                                                                                                        S                                                  3                          ,                          0                                                                                                                                    S                                                  3                          ,                          1                                                                                                                                    S                                                  3                          ,                          2                                                                                                                                    S                                                  3                          ,                          3                                                                                                                    ]                                                                                                                                                                                                                                                                                                        S                                                              1                                ,                                0                                                            2                                                        +                                                          S                                                              2                                ,                                0                                                            2                                                        +                                                          S                                                              3                                ,                                0                                                            2                                                                                =                          1                                                                                                                                                                                                                        S                                                              1                                ,                                1                                                            2                                                        +                                                          S                                                              2                                ,                                1                                                            2                                                        +                                                          S                                                              3                                ,                                1                                                            2                                                                                =                          1                                                                                                                                                                                                                                    S                                                  1                          ,                          2                                                2                                            +                                              S                                                  2                          ,                          2                                                2                                            +                                              S                                                  3                          ,                          2                                                2                                                              =                    1                                                                                                                                                            S                                      1                    ,                    3                                    2                                +                                  S                                      2                    ,                    3                                    2                                +                                  S                                      3                    ,                    3                                    2                                            =              1                                          The instrument matrix is calculated byA=I*S−1subsequently invertedB=A−1The polarimeter balanced in this way satisfies the relationship:S=B*I
However, such balancing does not ensure that this value is also determined for any other input polarisation with a DOP of 100% (DOP=1), because the polarisation and the detector signals contain errors. In B. Heffner, U.S. Pat. No. 5,296,913, a method is presented which can improve the existing calibration of a polarimeter with the help of at least three different polarisations of the same degree of polarisation. The improvement consists in the addition of a 4×4 correction matrix C.S=B*C*IThe correction matrix C has the shape of a diagonal matrix with the elements c0 . . . c3, and element c0 being equated with 1. Hence the correction consists in adding weighting factors c1, c2 and c3 to detector currents I1,I2and I3.       [                                        S            0                                                            S            1                                                            S            2                                                            S            3                                ]    =            [                                                  b              00                                                          b              01                                                          b              02                                                          b              03                                                                          b              10                                                          b              11                                                          b              12                                                          b              13                                                                          b              20                                                          b              21                                                          b              22                                                          b              23                                                                          b              30                                                          b              31                                                          b              32                                                          b              33                                          ]        *          [                                                  I              0                                                                                          c                1                            *                              I                1                                                                                                        c                2                            *                              I                2                                                                                                        c                3                            *                              I                3                                                        ]      With this method one succeeds in improving the accuracy of a polarimeter already calibrated.
According to Noé, R., DE 100 23 708 A 1, the instrument matrix of a polarimeter is found by employing for the calibration a large number of equally distributed states of polarisation. The calibration is based on the correlation of a large number of equally distributed polarisations for which a correlation matrix is known.
The calibration method according to Assam above requires exactly known input polarisations. The input polarisations are generated by a deterministic polarisation controller having a rotatable polariser and a rotatable λ/4 and a rotatable λ/2 wave plate, the accuracy being limited by mechanical faults of the rotatable devices, by imperfect optical elements and by possible faults of the optical coupling between the SOP generator and the polarimeter. A special problem is the exact determination of the delay of the wave plates used.
The polarimeter measures the four detector signals at the specified calibration SOPs. With these values the calibration matrix is determined, and the polarimeter thus clearly satisfies the requirements for SOP, DOP and power at exactly these values. Usually, however, the polarimeter shows measurement errors at all other polarisations, which become most clearly visible in a deviating degree of polarisation. The reason for this is that the four calibration SOPs were not known with sufficient accuracy and that the detector signals were not measured with sufficient precision.
The method for a verified post calibration of a polarimeter according to Heffner above uses the approach where the calibrated polarimeter has to show DOP=1 for all applied polarisations with DOP=1. The limits of this method lie in the simplicity of the correction values. While the three factors c1, c2 and c3 can correct the amount of the detector currents, they cannot correct the direction of the polarisations at which the detector currents I1,I2 and I3 reach their maximum and/or minimum. Polarimeters for which the polarisations, which lead to a maximum detector current, deviate from the polarisations of the base calibration, can only be corrected very imperfectly in this way. Effects of polarisers, whose transmission direction is unstable, or wave plates, whose delay is wave-dependent, cannot be corrected in this way.
The method according to Noé above requires the generation of a very large number of defined states of polarisation. The facilities needed for this are very costly. Also disadvantageous is the very long measuring time required for a very large number of polarisation measurements (in the order of magnitude of 200,000). Therefore a polarimeter that is calibrated with the help of fixed polarisation standards always shows measurement errors because the polarisations used for the calibration are incorrect. The errors in the polarimeter show most clearly in the display of the degree of polarisation DOP.
What is desired is a method of determining with high accuracy a calibration matrix for a polarimeter which provides improvements in the calibration of the polarimeter.